Problem: $z=-16i-92.3$ What are the real and imaginary parts of $z$ ? Choose 1 answer: Choose 1 answer: (Choice A) A $\text{Re}(z)=-16$ and $\text{Im}(z)=-92.3$ (Choice B) B $\text{Re}(z)=-92.3$ and $\text{Im}(z)=-16i$ (Choice C) C $\text{Re}(z)=-92.3$ and $\text{Im}(z)=-16$ (Choice D) D $\text{Re}(z)=-16i$ and $\text{Im}(z)=-92.3$
Answer: Background Complex numbers are numbers of the form $z={a}+{b}i$, where $i$ is the imaginary unit and ${a}$ and ${b}$ are real numbers. [What is the imaginary unit?] The real part of $z$ is denoted by $\text{Re}(z)={a}$. The imaginary part of $z$ is denoted by $\text{Im}(z)={b}.$ Finding the Real and Imaginary Parts of $z$ In this case, $z={-16}i-{92.3}$ is of the form ${b}i+{a}$, where ${a}={-92.3}$ and ${b}={-16}$. Therefore: $\text{Re}(z)={a}={-92.3}$. $\text{Im}(z)={b}={-16}$. Summary $\text{Re}(z)={-92.3}$ and $\text{Im}(z)={-16}$.